Nonlinear Langevin Equations for Wandering Patterns in Stochastic Neural Fields

DOI10.1137/140990371zbMath1402.92076arXiv1410.1475OpenAlexW2964276278MaRDI QIDQ5250031

Zachary P. Kilpatrick, Paul C. Bressloff

Publication date: 15 May 2015

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.1475

zbMATH Keywords

stochastic differential equationsphase-lockingneural fieldtraveling frontsspatially extended noise

Mathematics Subject Classification ID

Neural biology (92C20) PDEs with randomness, stochastic partial differential equations (35R60) Traveling wave solutions (35C07)

Related Items (14)

Velocity Integration in a Multilayer Neural Field Model of Spatial Working Memory ⋮ Synaptic efficacy shapes resource limitations in working memory ⋮ Distinct Excitatory and Inhibitory Bump Wandering in a Stochastic Neural Field ⋮ Ghosts of bump attractors in stochastic neural fields: bottlenecks and extinction ⋮ Phase Reduction of Waves, Patterns, and Oscillations Subject to Spatially Extended Noise ⋮ Sensory feedback in a bump attractor model of path integration ⋮ Stability of Traveling Waves for Reaction-Diffusion Equations with Multiplicative Noise ⋮ Stochastic neural field theory of wandering bumps on a sphere ⋮ A General Framework for Stochastic Traveling Waves and Patterns, with Application to Neural Field Equations ⋮ Stability of Traveling Waves for Systems of Reaction-Diffusion Equations with Multiplicative Noise ⋮ A Multiscale Analysis of Traveling Waves in Stochastic Neural Fields ⋮ Stability of Traveling Waves on Exponentially Long Timescales in Stochastic Reaction-Diffusion Equations ⋮ Stochastic Motion of Bumps in Planar Neural Fields ⋮ Wandering bumps in a stochastic neural field: a variational approach

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